Shadow not showing in Renderer
I have taken a look at your file. The transparent plane on which your shadow is casted has a setting for it to show or no to show shadows, and in which scenario.
Select that plane, go to the object settings on the right side and find this section:

In your case, only 'show in viewports' was ticked. You also need to tick the box that says 'show in renders' and your render will look the way you imagined it.
Good luck!